A generalized heat flux partitioning framework for directional heat transfer control in embedded heating systems using asymmetric thermal resistance design

Efficient utilization of thermal energy remains a major challenge in embedded heating systems because a significant portion of the generated heat is dissipated into the underlying structure rather than being delivered to the target surface. Existing studies have primarily focused on increasing heating capacity or reducing heat loss through insulation, whereas the directional control of conductive heat flow has received relatively little attention. This study proposes a generalized heat-flux partitioning framework based on asymmetric thermal resistance design to actively control the direction of conductive heat transfer in embedded heating systems. A representative stair geometry was employed only to define the computational domain, while the proposed framework is applicable to a broad range of embedded heating applications. Three representative thermal resistance configurations with different heating-element densities were systematically investigated using transient computational fluid dynamics (CFD) simulations. To quantify directional heating performance, a dimensionless heat-flux ratio ( η ) and dimensionless surface temperature ( θ ) were introduced. The results demonstrate that asymmetric thermal resistance effectively redistributes conductive heat toward the exposed surface, leading to faster surface heating, enhanced surface-directed heat transfer, and improved heating efficiency. Furthermore, all transient CFD results obtained from different thermal resistance configurations and heating-element densities collapse onto a single dimensionless scaling relationship when θ is plotted as a function of η . A quantitative regression analysis yielded an excellent agreement ( R ² = 0.995), confirming that the proposed heat-flux ratio serves as a robust reduced-order parameter governing the transient surface-heating performance. Rather than optimizing individual geometric parameters or insulation layouts, the proposed framework establishes a generalized thermal design methodology based on heat-flux partitioning and directional thermal resistance engineering. The proposed approach provides a scalable and application-independent strategy for improving the thermal performance of embedded heating systems in civil infrastructure, energy systems, and other solid-media heating applications.